Mathematics Articles - Page 1145 of 20

Bipartite Graph - If the vertex-set of a graph G can be split into two disjoint sets, V1 and V2 , in such a way that each edge in the graph joins a vertex in V1 to a vertex in V2 , and there are no edges in G that connect two vertices in V1 or two vertices in V2 , then the graph G is called a bipartite graph.Complete Bipartite Graph - A complete bipartite graph is a bipartite graph in which each vertex in the first set is joined to every single vertex in the second set. The ... Read More

Independent sets are represented in sets, in whichthere should not be any edges adjacent to each other. There should not be any common vertex between any two edges.there should not be any vertices adjacent to each other. There should not be any common edge between any two vertices.Independent Line SetLet 'G' = (V, E) be a graph. A subset L of E is called an independent line set of 'G' if no two edges in L are adjacent. Such a set is called an independent line set.ExampleLet us consider the following subsets −L1 = {a, b} L2 = {a, b} ... Read More

Independent sets are represented in sets, in whichthere should not be any edges adjacent to each other. There should not be any common vertex between any two edges.there should not be any vertices adjacent to each other. There should not be any common edge between any two vertices.Independent Vertex SetLet 'G' = (V, E) be a graph. A subset of 'V' is called an independent set of 'G' if no two vertices in 'S' are adjacent.ExampleConsider the following subsets from the above graphs −S1 = {e} S2 = {e, f} S3 = {a, g, c} S4 = {e, d}Clearly, S1 ... Read More

Measuring things and distances is one of the important concepts to learn when we are studying maths. For maximum uses, measuring scales do the work quite well and everyone is aware of it how to use one. But the measuring scale only provides a specific level of correctness and once you need exact measurements which lie between two spots on the scale it becomes difficult to get a correct reading without a bit of counterpart.Also measuring scales are very vulnerable to parallax mistakes which can cause a huge portion of the difference in readings from person to person which is ... Read More

Digital Computers use Binary number system to represent all types of information inside the computers. Alphanumeric characters are represented using binary bits (i.e., 0 and 1). Digital representations are easier to design, storage is easy, accuracy and precision are greater.There are various types of number representation techniques for digital number representation, for example: Binary number system, octal number system, decimal number system, and hexadecimal number system etc. But Binary number system is most relevant and popular for representing numbers in digital computer system.Storing Real NumberThese are structures as following below −There are two major approaches to store real numbers (i.e., ... Read More

Complements are used in digital computers in order to simply the subtraction operation and for the logical manipulations. For the Binary number (base-2) system, there are two types of complements: 1’s complement and 2’s complement.1’s Complement of a Binary NumberThere is a simple algorithm to convert a binary number into 1’s complement. To get 1’s complement of a binary number, simply invert the given number.2’s Complement of a Binary NumberThere is a simple algorithm to convert a binary number into 2’s complement. To get 2’s complement of a binary number, simply invert the given number and add 1 to the ... Read More

Binary Number System is one the type of most popular Number Representation techniques that used in digital systems. In the Binary System, there are only two symbols or possible digit values, i.e., 0 (off) and 1 (on). Represented by any device that only 2 operating states or possible conditions.Generally, there are two types of complement of Binary number: 1’s complement and 2’s complement. To get 1’s complement of a binary number, simply invert the given number. For example, 1’s complement of binary number 110010 is 001101. To get 2’s complement of binary number is 1’s complement of given number plus ... Read More

Negative numbers can be distinguishable with the help of extra bit or flag called sign bit or sign flag in Binary number representation system for signed numbers. It is not possible to add minus or plus symbol in front of a binary number because a binary number can have only two symbol either 0 or 1 for each position or bit. That’s why we use this extra bit called sign bit or sign flag. The value of sign bit is 1 for negative binary numbers and 0 for positive numbers.When an integer binary number is positive, the sign is represented ... Read More

A number system is a set of symbols used to represent values derived from a common base or radix. In a number, the value of each digit can be determined using digit, position of the digit in the number, and the base of the number system. The base is defined as the total number of digits are available in the number system. This is known as positional number system.Number SystemBaseDigit UsedBinary20, 1Octal80, 1, 2, 3, 4, 5, 6, 7Decimal100, 1, 2, 3, 4, 5, 6, 7, 8, 9Hexadecimal160, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, ... Read More

Zero (0) is used as a number and also as the numerical digit. Zero gives the additive identity of the integers, real numbers, and many algebraic structures. It is used as a placeholder for writing numbers.Natural numbers start from 1, then 2 and so on. We cannot count backward with them. Integers, on the other hand, allows us to count backward. Zero winds up being a good choice for the number that should come after 1 as we count backward. Integers can go in both directions, to a positive infinity and also in the reverse direction to a negative infinity. ... Read More